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b) Two buildings face each other on the opposite sides of the street. The angle of depression from the top of the taller building to the base of the other is 38ᵒ. The taller building is 30 m higher than the other building and the angle of depression from the top of the shorter to the base of the taller building is 23ᵒ. How wide is the street?

 Mar 16, 2016
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Let the height of the shorter building be h metres and the width of the street be w metres.

 

tan(38°) =  (h + 30)/w              (1)

tan(23°) =  h/w                        (2)

 

Subtract (2) from (1) to get    tan(38°) - tan(23°) = 30/w   so  w = 30/(tan(38°) - tan(23°))

 

I'll leave you to crunch the numbers.

 Mar 16, 2016

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